Editing Information content (section)

==== Information from sum of dice ====

The probability mass or density function (collectively [[probability measure]]) of the [[Sum of independent random variables|sum of two independent random variables]] [[Convolution#Convolution of measures|is the convolution of each probability measure]].  In the case of independent fair 6-sided dice rolls, the random variable <math> Z = X + Y</math> has probability mass function <math display="inline"> p_Z(z) = p_X(x) * p_Y(y) = {6 - |z - 7| \over 36} </math>, where <math> *</math> represents the [[discrete convolution]].  The [[Outcome (probability)|outcome]] <math> Z = 5 </math> has probability <math display="inline"> p_Z(5) = \frac{4}{36} = {1 \over 9} </math>. Therefore, the information asserted is<math display="block"> \operatorname{I}_Z(5) = -\log_2{\tfrac{1}{9}} = \log_2{9}
 \approx 3.169925 \text{ Sh}. 
</math>